ARCHIVED WIKISPACES DISCUSSION BELOW
Please do not add any new discussion to this archive page.
All new discussion should go on Talk:Height.
Applied to chords?
Are height formulas applied to chords, too? Or is this called something different?
Erlich talks about Sethares "dissonance" measure not really being dissonance because 4:5:6 and 1/4:1/5:1/6 measure the same but the major chord sounds more consonant than the minor, so he calls it "roughness" only, and it must be combined with "tonalness" (similarity to a harmonic series) to estimate a total "consonance".
"Unlike roughness, tonalness is not merely concerned with pairwise interactions of tones but three-way and higher interactions as well. A mathematical model for it is out of my grasp at the moment."
But 1/4:1/5:1/6 = 10:12:15, which *is* in the harmonic series (like every JI chord) but farther away from the root, so some kind of height function on the chord ratios would seem to fit the "tonalness" criteria.
- Omegatron September 10, 2014, 06:54:17 AM UTC-0700